Theme Essential Question: How can you analyze proportional relationships and use them to solve real-world and mathematical problems?
Essential Questions: How can you use proportions in scale drawings to solve problems?
Standards
7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
Objectives
The student will use proportional reasoning to solve scale drawing problems.
The student will use proportional reasoning to sketch figures at different scale factors.
The student will examine and conclude that the relationship between length of sides to perimeter to area of polygon is scale factor to scale factor to square scale factor.
The student will determine if two drawings are proportional by using their understanding of ratios and rates.
Background Information Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials at**http://www.azed.gov/educator-certification/**
Taken from Ohio Dept of Education Mathematics Model Curriculum 6-28-2022 Scale drawings of geometric figures connect understandings of proportionality to geometry and lead to future work in similarity and congruence. As an introduction to scale drawings in geometry, students should be given the opportunity to explore scale factor as the number of time you multiple the measure of one object to obtain the measure of a similar object. It is important that students first experience this concept concretely progressing to abstract contextual situations.
Pattern blocks (not the hexagon) provide a convenient means of developing the foundation of scale. Choosing one of the pattern blocks as an original shape, students can then create the next-size shape using only those same-shaped blocks. Questions about the relationship of the original block to the created shape should be asked and recorded. A sample of a recording sheet is shown.
This can be repeated for multiple iterations of each shape by comparing each side length to the original’s side length. An extension would be for students to compare the later iterations to the previous. Students should also be expected to use side lengths equal to fractional and decimal parts. In other words, if the original side can be stated to represent 2.5 inches, what would be the new lengths and what would be the scale?
After students have explored multiple iterations with a couple of shapes, ask them to choose and replicate a shape with given scales to find the new side lengths, as well as both the perimeters and areas. Starting with simple shapes and whole-number side lengths allows all students access to discover and understand the relationships. An interesting discovery is the relationship of the scale of the side lengths to the scale of the respective perimeters (same scale) and areas (scale squared). A sample recording sheet is shown.
Students should move on to drawing scaled figures on grid paper with proper figure labels, scale and dimensions. Provide word problems that require finding missing side lengths, perimeters or areas. For example, if a 4 by 4.5 cm rectangle is enlarged by a scale of 3, what will be the new perimeter? What is the new area? or If the scale is 6, what will the new side length look like? or Suppose the area of one triangle is 16 sq units and the scale factor between this triangle and a new triangle is 2.5. What is the area of the new triangle?
Reading scales on maps and determining the actual distance (length) is an appropriate contextual situation.
Assessment Product
The students will work in groups to design a gummi bear basketball court given the measure of a basketball court, basketball player’s height, and a gummi bear.
The drawing below shows the measurements for an NBA basketball court. The average basketball player on a team is 6' 6" tall. You are designing a basketball court for a Gummi Bear Team. Measure the Gummi Bear. http://www.uen.org/Lessonplan/preview.cgi?LPid=23378 (Gummy Bear Basketball)
Complete portfolio presentation and/or displays
Examine a map of Arkansas to determine distances between where you live and Fayetteville using a scale from the map. This distance will be used in the finally project for this unit in week 8.
Key Questions
How can you use scale drawings to find the actual dimensions of objects?
How can you tell if the scale is proportional or not?
What is the relationship between the scale drawing to actural dimensions with repect to length of side, perimeter of shape, and area of shape?
Observable Student Behaviors (Performance)
The student can work with scale factor of a scale drawing.
The student can provide a viable argument to explain the relationship between the length of side, perimeter of shape, and area of shape of a scale drawing and actual dimensions.
Mathematical Practices 1. Make sense of problems and persevere insolving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
Houghton Mifflin On Core Mathematics Middle School Grade 7 Unit 4.1, p. 89-92
ABC Mastering the Common Core in Mathematics
Chapter 11.11, p. 141
Chapter 11.12, p. 142
Chapter 11.13, p. 143-144
Gizmo Lessons
Perimeters and Areas of Similar Figures
Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity. Explore how the perimeters and areas of two similar figures compare.
Teaching the Common Core Math Standards with Hands-On Activities,
7.G.1 – Activity p. 114
Highly Recommended
http://illustrativemathematics.org/illustrations/107n (7.G.1) The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
Glencoe 7th Grade Mathematics Application and Concepts Course 2, Chapter 7.4, p. 304-309
Glencoe 7th Grade PreAlgebra, Chapter 6.3, p. 276-280
Mathematics in Children's Literature: Many children's books include math concepts and can be used to help teach them in a fun way. This website includes several annontated Lists of Children's Literature including the math concepts and grade levels.
The teaching Channel currently offers videos of K-12 mathematics teaching aligned with the Common Core Sate Standards, which would be perfect for professional development with teacher teams.
Interactivate is a set of free, online courseware for exploration in science and mathematics. It is comprised of activities, lessons, and discussions. The site is structured around collections of activities, lessons, and discussions.
The National Bank of Illuminations has been robbed! Students apply their knowledge of ratios, unit rates, and proportions to sort through the clues and deduce which suspect is the true culprit. Students will:
Practice computation of ratios, unit rates, and proportions
Grade: 7 Unit: 3 Week: 7 Dates: 1/7 – 1/11
Content: Scale Drawings
Theme Essential Question:
How can you analyze proportional relationships and use them to solve real-world and mathematical problems?
Essential Questions:
How can you use proportions in scale drawings to solve problems?
Standards
Objectives
Background Information
Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials at**http://www.azed.gov/educator-certification/**
Taken from Ohio Dept of Education Mathematics Model Curriculum 6-28-2022
Scale drawings of geometric figures connect understandings of proportionality to geometry and lead to future work in similarity and congruence. As an introduction to scale drawings in geometry, students should be given the opportunity to explore scale factor as the number of time you multiple the measure of one object to obtain the measure of a similar object. It is important that students first experience this concept concretely progressing to abstract contextual situations.
Pattern blocks (not the hexagon) provide a convenient means of developing the foundation of scale. Choosing one of the pattern blocks as an original shape, students can then create the next-size shape using only those same-shaped blocks. Questions about the relationship of the original block to the created shape should be asked and recorded. A sample of a recording sheet is shown.
This can be repeated for multiple iterations of each shape by comparing each side length to the original’s side length. An extension would be for students to compare the later iterations to the previous. Students should also be expected to use side lengths equal to fractional and decimal parts. In other words, if the original side can be stated to represent 2.5 inches, what would be the new lengths and what would be the scale?
After students have explored multiple iterations with a couple of shapes, ask them to choose and replicate a shape with given scales to find the new side lengths, as well as both the perimeters and areas. Starting with simple shapes and whole-number side lengths allows all students access to discover and understand the relationships. An interesting discovery is the relationship of the scale of the side lengths to the scale of the respective perimeters (same scale) and areas (scale squared). A sample recording sheet is shown.
Students should move on to drawing scaled figures on grid paper with proper figure labels, scale and dimensions. Provide word problems that require finding missing side lengths, perimeters or areas. For example, if a 4 by 4.5 cm rectangle is enlarged by a scale of 3, what will be the new perimeter? What is the new area? or If the scale is 6, what will the new side length look like? or Suppose the area of one triangle is 16 sq units and the scale factor between this triangle and a new triangle is 2.5. What is the area of the new triangle?
Reading scales on maps and determining the actual distance (length) is an appropriate contextual situation.
Assessment
Product
Key Questions
Observable Student Behaviors (Performance)
1. Make sense of problems and persevere insolving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Vocabulary
Scale
Ratios
Rates
Solving proportions
Suggested Activities:
- Houghton Mifflin On Core Mathematics Middle School Grade 7 Unit 4.1, p. 89-92
- ABC Mastering the Common Core in Mathematics
- Chapter 11.11, p. 141
- Chapter 11.12, p. 142
- Chapter 11.13, p. 143-144
- Gizmo Lessons
- Perimeters and Areas of Similar Figures
Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity. Explore how the perimeters and areas of two similar figures compare.- Teaching the Common Core Math Standards with Hands-On Activities,
- 7.G.1 – Activity p. 114
- Highly Recommended
http://illustrativemathematics.org/illustrations/107n (7.G.1)The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
Diverse Learners
Homework: (Teacher Discretion)
Terminology for Teachers:
Ethnicity/Culture | Immigration/Migration | Intercultural Competence | Socialization | Racism/Discrimination
High Yield Strategies
Similarities/Differences | Summarizing/Notetaking | Reinforcing/Recognition | Homework/Practice |
Non-Linguistic representation | Cooperative Learning | Objectives/Feedback |
Generating-Testing Hypothesis | Cues, Questions, Organizers
Resources:
Professional Texts:
Literary Texts
- High Noon: Math Adventure, Cut Down to Size By Scott Sundby
- Stretching and Shrinking By Lappan, Fey, Fitzgerald, Friel, and Phillips
- Measurement and children'e Literature/Ratios
http://sci.tamucc.edu/~eyoung/measure_literature.html- Mathematics in Children's Literature:
Click on the following link, http://libguides.nl.edu/mathinchildrenslit, then look under Math and Literature Bibliographies.Many children's books include math concepts and can be used to help teach them in a fun way. This website includes several annontated Lists of Children's Literature including the math concepts and grade levels.
- Middle & High School: Literature in Mathematics
Many books include websites with lesson ideas.http://sci.tamucc.edu/~eyoung/middle_school_literature.html
- Lesson Plans for Using Literature in Middle and High School Mathematics (developed by Leonor and edited by Elaine)
http://sci.tamucc.edu/~eyoung/Literature%20webpages/Leonor/index.html- Miscellaneous Math and Children's Literature
http://sci.tamucc.edu/~eyoung/literature.htmlInformational Texts
Art, Music, and Media
Manipulatives
Games
Videos
- Discovery Learning http://www.discoveryeducation.com/
- The Teaching Channel
- The teaching Channel currently offers videos of K-12 mathematics teaching aligned with the Common Core Sate Standards, which would be perfect for professional development with teacher teams.
https://www.teachingchannel.org/videos?categories=topics common-coreSMART Board Lesson, Promethean Lessons
Other Activities, etc.
- Activities and tools: http://www.shodor.org/interactivate/activities/
- Interactivate is a set of free, online courseware for exploration in science and mathematics. It is comprised of activities, lessons, and discussions. The site is structured around collections of activities, lessons, and discussions.
http://www.shodor.org/interactivate/guide/Students will:
Language
Arts
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Week 7
Week 8
7 Matrix
Accelerated 7
Matrix
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Week 7
Week 8
Home K-2
Home 3-6
Home 6-8
Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6